1 Data preparation

1.1 Outline

  • Load scripts: loads libraries and useful scripts used in the analyses; all .R files contained in scripts at the root of the factory are automatically loaded

  • Load data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.

1.2 Load packages


library(reportfactory)
library(here)
library(rio) 
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)

1.3 Load scripts

These scripts will load:

  • all scripts stored as .R files inside /scripts/
  • all scripts stored as .R files inside /src/

These scripts also contain routines to access the latest clean encrypted data (see next section).


reportfactory::rfh_load_scripts()

1.4 Load clean data

We import the latest NHS pathways data:


x <- import_pathways() %>%
  as_tibble()
x
## # A tibble: 164,924 x 11
##    site_type date       sex   age   ccg_code ccg_name count postcode nhs_region
##    <chr>     <date>     <chr> <chr> <chr>    <chr>    <int> <chr>    <chr>     
##  1 111       2020-03-18 fema… miss… e380000… nhs_glo…     1 gl34fe   South West
##  2 111       2020-03-18 fema… miss… e380001… nhs_sou…     1 ne325nn  North Eas…
##  3 111       2020-03-18 fema… 0-18  e380000… nhs_air…     8 bd57jr   North Eas…
##  4 111       2020-03-18 fema… 0-18  e380000… nhs_ash…     7 tn254ab  South East
##  5 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    35 rm13ae   London    
##  6 111       2020-03-18 fema… 0-18  e380000… nhs_bar…     9 n111np   London    
##  7 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    11 s752py   North Eas…
##  8 111       2020-03-18 fema… 0-18  e380000… nhs_bas…    19 ss143hg  East of E…
##  9 111       2020-03-18 fema… 0-18  e380000… nhs_bas…     6 dn227xf  North Eas…
## 10 111       2020-03-18 fema… 0-18  e380000… nhs_bat…     9 ba25rp   South West
## # … with 164,914 more rows, and 2 more variables: day <int>, weekday <fct>

We also import demographics data for NHS regions in England, used later in our analysis:


path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
##                  nhs_region variable      value
## 1                North West     0-18 0.22538599
## 2  North East and Yorkshire     0-18 0.21876449
## 3                  Midlands     0-18 0.22564656
## 4           East of England     0-18 0.22810783
## 5                    London     0-18 0.23764782
## 6                South East     0-18 0.22458811
## 7                South West     0-18 0.20799797
## 8                North West    19-69 0.64274078
## 9  North East and Yorkshire    19-69 0.64437753
## 10                 Midlands    19-69 0.63876675
## 11          East of England    19-69 0.63034229
## 12                   London    19-69 0.67820084
## 13               South East    19-69 0.63267336
## 14               South West    19-69 0.63176131
## 15               North West   70-120 0.13187323
## 16 North East and Yorkshire   70-120 0.13685797
## 17                 Midlands   70-120 0.13558669
## 18          East of England   70-120 0.14154988
## 19                   London   70-120 0.08415135
## 20               South East   70-120 0.14273853
## 21               South West   70-120 0.16024072

Finally, we import publically available deaths per NHS region:


dth <- import_deaths() %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

#truncation to account for reporting delay
delay_max <- 21

dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
##     date_report               nhs_region deaths
## 1    2020-03-01          East of England      0
## 2    2020-03-02          East of England      1
## 3    2020-03-03          East of England      0
## 4    2020-03-04          East of England      0
## 5    2020-03-05          East of England      0
## 6    2020-03-06          East of England      1
## 7    2020-03-07          East of England      0
## 8    2020-03-08          East of England      0
## 9    2020-03-09          East of England      1
## 10   2020-03-10          East of England      0
## 11   2020-03-11          East of England      0
## 12   2020-03-12          East of England      0
## 13   2020-03-13          East of England      1
## 14   2020-03-14          East of England      2
## 15   2020-03-15          East of England      2
## 16   2020-03-16          East of England      1
## 17   2020-03-17          East of England      1
## 18   2020-03-18          East of England      5
## 19   2020-03-19          East of England      4
## 20   2020-03-20          East of England      2
## 21   2020-03-21          East of England     11
## 22   2020-03-22          East of England     12
## 23   2020-03-23          East of England     11
## 24   2020-03-24          East of England     19
## 25   2020-03-25          East of England     26
## 26   2020-03-26          East of England     36
## 27   2020-03-27          East of England     38
## 28   2020-03-28          East of England     28
## 29   2020-03-29          East of England     43
## 30   2020-03-30          East of England     45
## 31   2020-03-31          East of England     70
## 32   2020-04-01          East of England     62
## 33   2020-04-02          East of England     64
## 34   2020-04-03          East of England     80
## 35   2020-04-04          East of England     71
## 36   2020-04-05          East of England     76
## 37   2020-04-06          East of England     71
## 38   2020-04-07          East of England     93
## 39   2020-04-08          East of England    111
## 40   2020-04-09          East of England     87
## 41   2020-04-10          East of England     74
## 42   2020-04-11          East of England     92
## 43   2020-04-12          East of England    101
## 44   2020-04-13          East of England     78
## 45   2020-04-14          East of England     61
## 46   2020-04-15          East of England     82
## 47   2020-04-16          East of England     74
## 48   2020-04-17          East of England     86
## 49   2020-04-18          East of England     64
## 50   2020-04-19          East of England     67
## 51   2020-04-20          East of England     67
## 52   2020-04-21          East of England     75
## 53   2020-04-22          East of England     67
## 54   2020-04-23          East of England     49
## 55   2020-04-24          East of England     66
## 56   2020-04-25          East of England     54
## 57   2020-04-26          East of England     48
## 58   2020-04-27          East of England     46
## 59   2020-04-28          East of England     58
## 60   2020-04-29          East of England     32
## 61   2020-04-30          East of England     45
## 62   2020-05-01          East of England     49
## 63   2020-05-02          East of England     29
## 64   2020-05-03          East of England     41
## 65   2020-05-04          East of England     19
## 66   2020-05-05          East of England     36
## 67   2020-05-06          East of England     31
## 68   2020-05-07          East of England     33
## 69   2020-05-08          East of England     33
## 70   2020-05-09          East of England     29
## 71   2020-05-10          East of England     22
## 72   2020-05-11          East of England     18
## 73   2020-05-12          East of England     21
## 74   2020-05-13          East of England     27
## 75   2020-05-14          East of England     26
## 76   2020-05-15          East of England     19
## 77   2020-05-16          East of England     26
## 78   2020-05-17          East of England     17
## 79   2020-05-18          East of England     25
## 80   2020-05-19          East of England     15
## 81   2020-05-20          East of England     26
## 82   2020-05-21          East of England     21
## 83   2020-05-22          East of England     13
## 84   2020-05-23          East of England     12
## 85   2020-05-24          East of England     17
## 86   2020-05-25          East of England     25
## 87   2020-05-26          East of England     14
## 88   2020-05-27          East of England     12
## 89   2020-05-28          East of England     17
## 90   2020-05-29          East of England     16
## 91   2020-05-30          East of England      9
## 92   2020-05-31          East of England      8
## 93   2020-06-01          East of England     17
## 94   2020-06-02          East of England     14
## 95   2020-06-03          East of England     10
## 96   2020-06-04          East of England      7
## 97   2020-06-05          East of England     14
## 98   2020-06-06          East of England      5
## 99   2020-06-07          East of England      9
## 100  2020-06-08          East of England      7
## 101  2020-06-09          East of England      6
## 102  2020-06-10          East of England      8
## 103  2020-06-11          East of England      1
## 104  2020-06-12          East of England      9
## 105  2020-06-13          East of England      5
## 106  2020-06-14          East of England      4
## 107  2020-06-15          East of England      8
## 108  2020-06-16          East of England      3
## 109  2020-06-17          East of England      7
## 110  2020-06-18          East of England      4
## 111  2020-06-19          East of England      7
## 112  2020-06-20          East of England      4
## 113  2020-06-21          East of England      3
## 114  2020-06-22          East of England      6
## 115  2020-06-23          East of England      4
## 116  2020-06-24          East of England      4
## 117  2020-06-25          East of England      1
## 118  2020-06-26          East of England      5
## 119  2020-06-27          East of England      6
## 120  2020-06-28          East of England      8
## 121  2020-06-29          East of England      4
## 122  2020-06-30          East of England      4
## 123  2020-07-01          East of England      2
## 124  2020-07-02          East of England      4
## 125  2020-07-03          East of England      0
## 126  2020-03-01                   London      0
## 127  2020-03-02                   London      0
## 128  2020-03-03                   London      0
## 129  2020-03-04                   London      0
## 130  2020-03-05                   London      0
## 131  2020-03-06                   London      1
## 132  2020-03-07                   London      0
## 133  2020-03-08                   London      0
## 134  2020-03-09                   London      1
## 135  2020-03-10                   London      0
## 136  2020-03-11                   London      6
## 137  2020-03-12                   London      6
## 138  2020-03-13                   London     10
## 139  2020-03-14                   London     14
## 140  2020-03-15                   London     10
## 141  2020-03-16                   London     15
## 142  2020-03-17                   London     23
## 143  2020-03-18                   London     27
## 144  2020-03-19                   London     25
## 145  2020-03-20                   London     44
## 146  2020-03-21                   London     49
## 147  2020-03-22                   London     54
## 148  2020-03-23                   London     63
## 149  2020-03-24                   London     87
## 150  2020-03-25                   London    113
## 151  2020-03-26                   London    129
## 152  2020-03-27                   London    130
## 153  2020-03-28                   London    122
## 154  2020-03-29                   London    146
## 155  2020-03-30                   London    149
## 156  2020-03-31                   London    181
## 157  2020-04-01                   London    202
## 158  2020-04-02                   London    191
## 159  2020-04-03                   London    196
## 160  2020-04-04                   London    230
## 161  2020-04-05                   London    195
## 162  2020-04-06                   London    197
## 163  2020-04-07                   London    220
## 164  2020-04-08                   London    238
## 165  2020-04-09                   London    206
## 166  2020-04-10                   London    170
## 167  2020-04-11                   London    178
## 168  2020-04-12                   London    158
## 169  2020-04-13                   London    166
## 170  2020-04-14                   London    144
## 171  2020-04-15                   London    142
## 172  2020-04-16                   London    140
## 173  2020-04-17                   London    100
## 174  2020-04-18                   London    101
## 175  2020-04-19                   London    103
## 176  2020-04-20                   London     95
## 177  2020-04-21                   London     94
## 178  2020-04-22                   London    109
## 179  2020-04-23                   London     77
## 180  2020-04-24                   London     71
## 181  2020-04-25                   London     58
## 182  2020-04-26                   London     53
## 183  2020-04-27                   London     51
## 184  2020-04-28                   London     44
## 185  2020-04-29                   London     44
## 186  2020-04-30                   London     40
## 187  2020-05-01                   London     41
## 188  2020-05-02                   London     41
## 189  2020-05-03                   London     36
## 190  2020-05-04                   London     30
## 191  2020-05-05                   London     25
## 192  2020-05-06                   London     37
## 193  2020-05-07                   London     37
## 194  2020-05-08                   London     30
## 195  2020-05-09                   London     23
## 196  2020-05-10                   London     26
## 197  2020-05-11                   London     18
## 198  2020-05-12                   London     18
## 199  2020-05-13                   London     17
## 200  2020-05-14                   London     20
## 201  2020-05-15                   London     18
## 202  2020-05-16                   London     14
## 203  2020-05-17                   London     15
## 204  2020-05-18                   London      9
## 205  2020-05-19                   London     14
## 206  2020-05-20                   London     19
## 207  2020-05-21                   London     12
## 208  2020-05-22                   London     10
## 209  2020-05-23                   London      6
## 210  2020-05-24                   London      7
## 211  2020-05-25                   London      9
## 212  2020-05-26                   London     13
## 213  2020-05-27                   London      7
## 214  2020-05-28                   London      8
## 215  2020-05-29                   London      7
## 216  2020-05-30                   London     12
## 217  2020-05-31                   London      6
## 218  2020-06-01                   London     10
## 219  2020-06-02                   London      7
## 220  2020-06-03                   London      6
## 221  2020-06-04                   London      8
## 222  2020-06-05                   London      4
## 223  2020-06-06                   London      0
## 224  2020-06-07                   London      5
## 225  2020-06-08                   London      5
## 226  2020-06-09                   London      4
## 227  2020-06-10                   London      7
## 228  2020-06-11                   London      5
## 229  2020-06-12                   London      3
## 230  2020-06-13                   London      3
## 231  2020-06-14                   London      3
## 232  2020-06-15                   London      1
## 233  2020-06-16                   London      2
## 234  2020-06-17                   London      1
## 235  2020-06-18                   London      2
## 236  2020-06-19                   London      3
## 237  2020-06-20                   London      3
## 238  2020-06-21                   London      4
## 239  2020-06-22                   London      2
## 240  2020-06-23                   London      1
## 241  2020-06-24                   London      4
## 242  2020-06-25                   London      3
## 243  2020-06-26                   London      2
## 244  2020-06-27                   London      1
## 245  2020-06-28                   London      2
## 246  2020-06-29                   London      2
## 247  2020-06-30                   London      1
## 248  2020-07-01                   London      1
## 249  2020-07-02                   London      1
## 250  2020-07-03                   London      0
## 251  2020-03-01                 Midlands      0
## 252  2020-03-02                 Midlands      0
## 253  2020-03-03                 Midlands      1
## 254  2020-03-04                 Midlands      0
## 255  2020-03-05                 Midlands      0
## 256  2020-03-06                 Midlands      0
## 257  2020-03-07                 Midlands      0
## 258  2020-03-08                 Midlands      3
## 259  2020-03-09                 Midlands      1
## 260  2020-03-10                 Midlands      0
## 261  2020-03-11                 Midlands      2
## 262  2020-03-12                 Midlands      6
## 263  2020-03-13                 Midlands      5
## 264  2020-03-14                 Midlands      4
## 265  2020-03-15                 Midlands      5
## 266  2020-03-16                 Midlands     11
## 267  2020-03-17                 Midlands      8
## 268  2020-03-18                 Midlands     13
## 269  2020-03-19                 Midlands      8
## 270  2020-03-20                 Midlands     28
## 271  2020-03-21                 Midlands     13
## 272  2020-03-22                 Midlands     31
## 273  2020-03-23                 Midlands     33
## 274  2020-03-24                 Midlands     41
## 275  2020-03-25                 Midlands     48
## 276  2020-03-26                 Midlands     64
## 277  2020-03-27                 Midlands     72
## 278  2020-03-28                 Midlands     89
## 279  2020-03-29                 Midlands     92
## 280  2020-03-30                 Midlands     90
## 281  2020-03-31                 Midlands    123
## 282  2020-04-01                 Midlands    140
## 283  2020-04-02                 Midlands    142
## 284  2020-04-03                 Midlands    124
## 285  2020-04-04                 Midlands    151
## 286  2020-04-05                 Midlands    164
## 287  2020-04-06                 Midlands    140
## 288  2020-04-07                 Midlands    123
## 289  2020-04-08                 Midlands    186
## 290  2020-04-09                 Midlands    139
## 291  2020-04-10                 Midlands    127
## 292  2020-04-11                 Midlands    142
## 293  2020-04-12                 Midlands    139
## 294  2020-04-13                 Midlands    120
## 295  2020-04-14                 Midlands    116
## 296  2020-04-15                 Midlands    147
## 297  2020-04-16                 Midlands    102
## 298  2020-04-17                 Midlands    118
## 299  2020-04-18                 Midlands    115
## 300  2020-04-19                 Midlands     92
## 301  2020-04-20                 Midlands    107
## 302  2020-04-21                 Midlands     86
## 303  2020-04-22                 Midlands     78
## 304  2020-04-23                 Midlands    103
## 305  2020-04-24                 Midlands     79
## 306  2020-04-25                 Midlands     72
## 307  2020-04-26                 Midlands     81
## 308  2020-04-27                 Midlands     74
## 309  2020-04-28                 Midlands     68
## 310  2020-04-29                 Midlands     53
## 311  2020-04-30                 Midlands     56
## 312  2020-05-01                 Midlands     64
## 313  2020-05-02                 Midlands     51
## 314  2020-05-03                 Midlands     52
## 315  2020-05-04                 Midlands     61
## 316  2020-05-05                 Midlands     59
## 317  2020-05-06                 Midlands     59
## 318  2020-05-07                 Midlands     48
## 319  2020-05-08                 Midlands     34
## 320  2020-05-09                 Midlands     37
## 321  2020-05-10                 Midlands     42
## 322  2020-05-11                 Midlands     33
## 323  2020-05-12                 Midlands     45
## 324  2020-05-13                 Midlands     40
## 325  2020-05-14                 Midlands     37
## 326  2020-05-15                 Midlands     40
## 327  2020-05-16                 Midlands     34
## 328  2020-05-17                 Midlands     31
## 329  2020-05-18                 Midlands     34
## 330  2020-05-19                 Midlands     34
## 331  2020-05-20                 Midlands     36
## 332  2020-05-21                 Midlands     32
## 333  2020-05-22                 Midlands     27
## 334  2020-05-23                 Midlands     34
## 335  2020-05-24                 Midlands     19
## 336  2020-05-25                 Midlands     26
## 337  2020-05-26                 Midlands     33
## 338  2020-05-27                 Midlands     29
## 339  2020-05-28                 Midlands     28
## 340  2020-05-29                 Midlands     20
## 341  2020-05-30                 Midlands     20
## 342  2020-05-31                 Midlands     22
## 343  2020-06-01                 Midlands     20
## 344  2020-06-02                 Midlands     22
## 345  2020-06-03                 Midlands     24
## 346  2020-06-04                 Midlands     16
## 347  2020-06-05                 Midlands     21
## 348  2020-06-06                 Midlands     20
## 349  2020-06-07                 Midlands     17
## 350  2020-06-08                 Midlands     16
## 351  2020-06-09                 Midlands     18
## 352  2020-06-10                 Midlands     15
## 353  2020-06-11                 Midlands     13
## 354  2020-06-12                 Midlands     12
## 355  2020-06-13                 Midlands      6
## 356  2020-06-14                 Midlands     18
## 357  2020-06-15                 Midlands     12
## 358  2020-06-16                 Midlands     15
## 359  2020-06-17                 Midlands     10
## 360  2020-06-18                 Midlands     15
## 361  2020-06-19                 Midlands      9
## 362  2020-06-20                 Midlands     15
## 363  2020-06-21                 Midlands     13
## 364  2020-06-22                 Midlands     13
## 365  2020-06-23                 Midlands     17
## 366  2020-06-24                 Midlands     14
## 367  2020-06-25                 Midlands     17
## 368  2020-06-26                 Midlands      5
## 369  2020-06-27                 Midlands      4
## 370  2020-06-28                 Midlands      6
## 371  2020-06-29                 Midlands      6
## 372  2020-06-30                 Midlands      5
## 373  2020-07-01                 Midlands      6
## 374  2020-07-02                 Midlands      5
## 375  2020-07-03                 Midlands      0
## 376  2020-03-01 North East and Yorkshire      0
## 377  2020-03-02 North East and Yorkshire      0
## 378  2020-03-03 North East and Yorkshire      0
## 379  2020-03-04 North East and Yorkshire      0
## 380  2020-03-05 North East and Yorkshire      0
## 381  2020-03-06 North East and Yorkshire      0
## 382  2020-03-07 North East and Yorkshire      0
## 383  2020-03-08 North East and Yorkshire      0
## 384  2020-03-09 North East and Yorkshire      0
## 385  2020-03-10 North East and Yorkshire      0
## 386  2020-03-11 North East and Yorkshire      0
## 387  2020-03-12 North East and Yorkshire      0
## 388  2020-03-13 North East and Yorkshire      0
## 389  2020-03-14 North East and Yorkshire      0
## 390  2020-03-15 North East and Yorkshire      2
## 391  2020-03-16 North East and Yorkshire      3
## 392  2020-03-17 North East and Yorkshire      1
## 393  2020-03-18 North East and Yorkshire      2
## 394  2020-03-19 North East and Yorkshire      6
## 395  2020-03-20 North East and Yorkshire      5
## 396  2020-03-21 North East and Yorkshire      6
## 397  2020-03-22 North East and Yorkshire      7
## 398  2020-03-23 North East and Yorkshire      9
## 399  2020-03-24 North East and Yorkshire      8
## 400  2020-03-25 North East and Yorkshire     18
## 401  2020-03-26 North East and Yorkshire     21
## 402  2020-03-27 North East and Yorkshire     28
## 403  2020-03-28 North East and Yorkshire     35
## 404  2020-03-29 North East and Yorkshire     38
## 405  2020-03-30 North East and Yorkshire     64
## 406  2020-03-31 North East and Yorkshire     60
## 407  2020-04-01 North East and Yorkshire     67
## 408  2020-04-02 North East and Yorkshire     75
## 409  2020-04-03 North East and Yorkshire    100
## 410  2020-04-04 North East and Yorkshire    105
## 411  2020-04-05 North East and Yorkshire     92
## 412  2020-04-06 North East and Yorkshire     96
## 413  2020-04-07 North East and Yorkshire    102
## 414  2020-04-08 North East and Yorkshire    107
## 415  2020-04-09 North East and Yorkshire    111
## 416  2020-04-10 North East and Yorkshire    117
## 417  2020-04-11 North East and Yorkshire     98
## 418  2020-04-12 North East and Yorkshire     84
## 419  2020-04-13 North East and Yorkshire     94
## 420  2020-04-14 North East and Yorkshire    107
## 421  2020-04-15 North East and Yorkshire     96
## 422  2020-04-16 North East and Yorkshire    103
## 423  2020-04-17 North East and Yorkshire     88
## 424  2020-04-18 North East and Yorkshire     95
## 425  2020-04-19 North East and Yorkshire     88
## 426  2020-04-20 North East and Yorkshire    100
## 427  2020-04-21 North East and Yorkshire     76
## 428  2020-04-22 North East and Yorkshire     84
## 429  2020-04-23 North East and Yorkshire     63
## 430  2020-04-24 North East and Yorkshire     72
## 431  2020-04-25 North East and Yorkshire     69
## 432  2020-04-26 North East and Yorkshire     65
## 433  2020-04-27 North East and Yorkshire     65
## 434  2020-04-28 North East and Yorkshire     57
## 435  2020-04-29 North East and Yorkshire     69
## 436  2020-04-30 North East and Yorkshire     57
## 437  2020-05-01 North East and Yorkshire     64
## 438  2020-05-02 North East and Yorkshire     48
## 439  2020-05-03 North East and Yorkshire     40
## 440  2020-05-04 North East and Yorkshire     49
## 441  2020-05-05 North East and Yorkshire     40
## 442  2020-05-06 North East and Yorkshire     51
## 443  2020-05-07 North East and Yorkshire     45
## 444  2020-05-08 North East and Yorkshire     42
## 445  2020-05-09 North East and Yorkshire     44
## 446  2020-05-10 North East and Yorkshire     40
## 447  2020-05-11 North East and Yorkshire     29
## 448  2020-05-12 North East and Yorkshire     27
## 449  2020-05-13 North East and Yorkshire     28
## 450  2020-05-14 North East and Yorkshire     31
## 451  2020-05-15 North East and Yorkshire     32
## 452  2020-05-16 North East and Yorkshire     35
## 453  2020-05-17 North East and Yorkshire     26
## 454  2020-05-18 North East and Yorkshire     30
## 455  2020-05-19 North East and Yorkshire     27
## 456  2020-05-20 North East and Yorkshire     22
## 457  2020-05-21 North East and Yorkshire     33
## 458  2020-05-22 North East and Yorkshire     22
## 459  2020-05-23 North East and Yorkshire     18
## 460  2020-05-24 North East and Yorkshire     26
## 461  2020-05-25 North East and Yorkshire     21
## 462  2020-05-26 North East and Yorkshire     21
## 463  2020-05-27 North East and Yorkshire     22
## 464  2020-05-28 North East and Yorkshire     21
## 465  2020-05-29 North East and Yorkshire     25
## 466  2020-05-30 North East and Yorkshire     20
## 467  2020-05-31 North East and Yorkshire     20
## 468  2020-06-01 North East and Yorkshire     17
## 469  2020-06-02 North East and Yorkshire     23
## 470  2020-06-03 North East and Yorkshire     23
## 471  2020-06-04 North East and Yorkshire     17
## 472  2020-06-05 North East and Yorkshire     18
## 473  2020-06-06 North East and Yorkshire     21
## 474  2020-06-07 North East and Yorkshire     14
## 475  2020-06-08 North East and Yorkshire     11
## 476  2020-06-09 North East and Yorkshire     12
## 477  2020-06-10 North East and Yorkshire     19
## 478  2020-06-11 North East and Yorkshire      7
## 479  2020-06-12 North East and Yorkshire      9
## 480  2020-06-13 North East and Yorkshire     10
## 481  2020-06-14 North East and Yorkshire     11
## 482  2020-06-15 North East and Yorkshire      9
## 483  2020-06-16 North East and Yorkshire     10
## 484  2020-06-17 North East and Yorkshire      9
## 485  2020-06-18 North East and Yorkshire     10
## 486  2020-06-19 North East and Yorkshire      6
## 487  2020-06-20 North East and Yorkshire      4
## 488  2020-06-21 North East and Yorkshire      4
## 489  2020-06-22 North East and Yorkshire      6
## 490  2020-06-23 North East and Yorkshire      7
## 491  2020-06-24 North East and Yorkshire     10
## 492  2020-06-25 North East and Yorkshire      3
## 493  2020-06-26 North East and Yorkshire      7
## 494  2020-06-27 North East and Yorkshire      3
## 495  2020-06-28 North East and Yorkshire      4
## 496  2020-06-29 North East and Yorkshire      2
## 497  2020-06-30 North East and Yorkshire      4
## 498  2020-07-01 North East and Yorkshire      1
## 499  2020-07-02 North East and Yorkshire      3
## 500  2020-07-03 North East and Yorkshire      1
## 501  2020-03-01               North West      0
## 502  2020-03-02               North West      0
## 503  2020-03-03               North West      0
## 504  2020-03-04               North West      0
## 505  2020-03-05               North West      1
## 506  2020-03-06               North West      0
## 507  2020-03-07               North West      0
## 508  2020-03-08               North West      1
## 509  2020-03-09               North West      0
## 510  2020-03-10               North West      0
## 511  2020-03-11               North West      0
## 512  2020-03-12               North West      2
## 513  2020-03-13               North West      3
## 514  2020-03-14               North West      1
## 515  2020-03-15               North West      4
## 516  2020-03-16               North West      2
## 517  2020-03-17               North West      4
## 518  2020-03-18               North West      6
## 519  2020-03-19               North West      7
## 520  2020-03-20               North West     10
## 521  2020-03-21               North West     11
## 522  2020-03-22               North West     13
## 523  2020-03-23               North West     15
## 524  2020-03-24               North West     21
## 525  2020-03-25               North West     21
## 526  2020-03-26               North West     29
## 527  2020-03-27               North West     36
## 528  2020-03-28               North West     28
## 529  2020-03-29               North West     46
## 530  2020-03-30               North West     67
## 531  2020-03-31               North West     52
## 532  2020-04-01               North West     86
## 533  2020-04-02               North West     96
## 534  2020-04-03               North West     95
## 535  2020-04-04               North West     98
## 536  2020-04-05               North West    102
## 537  2020-04-06               North West    100
## 538  2020-04-07               North West    135
## 539  2020-04-08               North West    127
## 540  2020-04-09               North West    119
## 541  2020-04-10               North West    117
## 542  2020-04-11               North West    138
## 543  2020-04-12               North West    125
## 544  2020-04-13               North West    129
## 545  2020-04-14               North West    131
## 546  2020-04-15               North West    114
## 547  2020-04-16               North West    135
## 548  2020-04-17               North West     98
## 549  2020-04-18               North West    113
## 550  2020-04-19               North West     71
## 551  2020-04-20               North West     83
## 552  2020-04-21               North West     76
## 553  2020-04-22               North West     86
## 554  2020-04-23               North West     85
## 555  2020-04-24               North West     66
## 556  2020-04-25               North West     66
## 557  2020-04-26               North West     55
## 558  2020-04-27               North West     54
## 559  2020-04-28               North West     57
## 560  2020-04-29               North West     63
## 561  2020-04-30               North West     59
## 562  2020-05-01               North West     45
## 563  2020-05-02               North West     56
## 564  2020-05-03               North West     55
## 565  2020-05-04               North West     48
## 566  2020-05-05               North West     48
## 567  2020-05-06               North West     44
## 568  2020-05-07               North West     49
## 569  2020-05-08               North West     42
## 570  2020-05-09               North West     30
## 571  2020-05-10               North West     41
## 572  2020-05-11               North West     35
## 573  2020-05-12               North West     38
## 574  2020-05-13               North West     25
## 575  2020-05-14               North West     26
## 576  2020-05-15               North West     33
## 577  2020-05-16               North West     32
## 578  2020-05-17               North West     24
## 579  2020-05-18               North West     31
## 580  2020-05-19               North West     35
## 581  2020-05-20               North West     27
## 582  2020-05-21               North West     27
## 583  2020-05-22               North West     26
## 584  2020-05-23               North West     31
## 585  2020-05-24               North West     26
## 586  2020-05-25               North West     31
## 587  2020-05-26               North West     27
## 588  2020-05-27               North West     27
## 589  2020-05-28               North West     28
## 590  2020-05-29               North West     20
## 591  2020-05-30               North West     19
## 592  2020-05-31               North West     13
## 593  2020-06-01               North West     12
## 594  2020-06-02               North West     27
## 595  2020-06-03               North West     22
## 596  2020-06-04               North West     22
## 597  2020-06-05               North West     16
## 598  2020-06-06               North West     26
## 599  2020-06-07               North West     20
## 600  2020-06-08               North West     23
## 601  2020-06-09               North West     17
## 602  2020-06-10               North West     16
## 603  2020-06-11               North West     16
## 604  2020-06-12               North West     11
## 605  2020-06-13               North West     10
## 606  2020-06-14               North West     15
## 607  2020-06-15               North West     16
## 608  2020-06-16               North West     15
## 609  2020-06-17               North West     12
## 610  2020-06-18               North West     13
## 611  2020-06-19               North West      7
## 612  2020-06-20               North West     11
## 613  2020-06-21               North West      7
## 614  2020-06-22               North West     11
## 615  2020-06-23               North West     13
## 616  2020-06-24               North West     13
## 617  2020-06-25               North West     14
## 618  2020-06-26               North West      5
## 619  2020-06-27               North West      7
## 620  2020-06-28               North West      8
## 621  2020-06-29               North West      4
## 622  2020-06-30               North West      6
## 623  2020-07-01               North West      2
## 624  2020-07-02               North West      5
## 625  2020-07-03               North West      1
## 626  2020-03-01               South East      0
## 627  2020-03-02               South East      0
## 628  2020-03-03               South East      1
## 629  2020-03-04               South East      0
## 630  2020-03-05               South East      1
## 631  2020-03-06               South East      0
## 632  2020-03-07               South East      0
## 633  2020-03-08               South East      1
## 634  2020-03-09               South East      1
## 635  2020-03-10               South East      1
## 636  2020-03-11               South East      1
## 637  2020-03-12               South East      0
## 638  2020-03-13               South East      1
## 639  2020-03-14               South East      1
## 640  2020-03-15               South East      5
## 641  2020-03-16               South East      8
## 642  2020-03-17               South East      7
## 643  2020-03-18               South East     10
## 644  2020-03-19               South East      9
## 645  2020-03-20               South East     13
## 646  2020-03-21               South East      7
## 647  2020-03-22               South East     25
## 648  2020-03-23               South East     20
## 649  2020-03-24               South East     22
## 650  2020-03-25               South East     29
## 651  2020-03-26               South East     35
## 652  2020-03-27               South East     34
## 653  2020-03-28               South East     36
## 654  2020-03-29               South East     55
## 655  2020-03-30               South East     58
## 656  2020-03-31               South East     65
## 657  2020-04-01               South East     66
## 658  2020-04-02               South East     55
## 659  2020-04-03               South East     72
## 660  2020-04-04               South East     80
## 661  2020-04-05               South East     82
## 662  2020-04-06               South East     88
## 663  2020-04-07               South East    100
## 664  2020-04-08               South East     83
## 665  2020-04-09               South East    104
## 666  2020-04-10               South East     88
## 667  2020-04-11               South East     88
## 668  2020-04-12               South East     88
## 669  2020-04-13               South East     84
## 670  2020-04-14               South East     65
## 671  2020-04-15               South East     72
## 672  2020-04-16               South East     56
## 673  2020-04-17               South East     86
## 674  2020-04-18               South East     57
## 675  2020-04-19               South East     70
## 676  2020-04-20               South East     87
## 677  2020-04-21               South East     51
## 678  2020-04-22               South East     54
## 679  2020-04-23               South East     57
## 680  2020-04-24               South East     64
## 681  2020-04-25               South East     51
## 682  2020-04-26               South East     51
## 683  2020-04-27               South East     40
## 684  2020-04-28               South East     40
## 685  2020-04-29               South East     47
## 686  2020-04-30               South East     29
## 687  2020-05-01               South East     37
## 688  2020-05-02               South East     36
## 689  2020-05-03               South East     17
## 690  2020-05-04               South East     35
## 691  2020-05-05               South East     29
## 692  2020-05-06               South East     25
## 693  2020-05-07               South East     27
## 694  2020-05-08               South East     26
## 695  2020-05-09               South East     28
## 696  2020-05-10               South East     19
## 697  2020-05-11               South East     25
## 698  2020-05-12               South East     27
## 699  2020-05-13               South East     18
## 700  2020-05-14               South East     32
## 701  2020-05-15               South East     25
## 702  2020-05-16               South East     22
## 703  2020-05-17               South East     18
## 704  2020-05-18               South East     22
## 705  2020-05-19               South East     12
## 706  2020-05-20               South East     22
## 707  2020-05-21               South East     15
## 708  2020-05-22               South East     17
## 709  2020-05-23               South East     21
## 710  2020-05-24               South East     17
## 711  2020-05-25               South East     13
## 712  2020-05-26               South East     19
## 713  2020-05-27               South East     18
## 714  2020-05-28               South East     12
## 715  2020-05-29               South East     21
## 716  2020-05-30               South East      8
## 717  2020-05-31               South East     12
## 718  2020-06-01               South East     11
## 719  2020-06-02               South East     13
## 720  2020-06-03               South East     18
## 721  2020-06-04               South East     11
## 722  2020-06-05               South East     11
## 723  2020-06-06               South East     10
## 724  2020-06-07               South East     12
## 725  2020-06-08               South East      8
## 726  2020-06-09               South East     10
## 727  2020-06-10               South East     11
## 728  2020-06-11               South East      5
## 729  2020-06-12               South East      6
## 730  2020-06-13               South East      6
## 731  2020-06-14               South East      7
## 732  2020-06-15               South East      8
## 733  2020-06-16               South East     12
## 734  2020-06-17               South East      9
## 735  2020-06-18               South East      4
## 736  2020-06-19               South East      6
## 737  2020-06-20               South East      5
## 738  2020-06-21               South East      3
## 739  2020-06-22               South East      2
## 740  2020-06-23               South East      8
## 741  2020-06-24               South East      6
## 742  2020-06-25               South East      4
## 743  2020-06-26               South East      7
## 744  2020-06-27               South East      7
## 745  2020-06-28               South East      6
## 746  2020-06-29               South East      5
## 747  2020-06-30               South East      5
## 748  2020-07-01               South East      1
## 749  2020-07-02               South East      1
## 750  2020-07-03               South East      0
## 751  2020-03-01               South West      0
## 752  2020-03-02               South West      0
## 753  2020-03-03               South West      0
## 754  2020-03-04               South West      0
## 755  2020-03-05               South West      0
## 756  2020-03-06               South West      0
## 757  2020-03-07               South West      0
## 758  2020-03-08               South West      0
## 759  2020-03-09               South West      0
## 760  2020-03-10               South West      0
## 761  2020-03-11               South West      1
## 762  2020-03-12               South West      0
## 763  2020-03-13               South West      0
## 764  2020-03-14               South West      1
## 765  2020-03-15               South West      0
## 766  2020-03-16               South West      0
## 767  2020-03-17               South West      2
## 768  2020-03-18               South West      2
## 769  2020-03-19               South West      4
## 770  2020-03-20               South West      3
## 771  2020-03-21               South West      6
## 772  2020-03-22               South West      7
## 773  2020-03-23               South West      8
## 774  2020-03-24               South West      7
## 775  2020-03-25               South West      9
## 776  2020-03-26               South West     11
## 777  2020-03-27               South West     13
## 778  2020-03-28               South West     21
## 779  2020-03-29               South West     18
## 780  2020-03-30               South West     23
## 781  2020-03-31               South West     23
## 782  2020-04-01               South West     22
## 783  2020-04-02               South West     23
## 784  2020-04-03               South West     30
## 785  2020-04-04               South West     42
## 786  2020-04-05               South West     32
## 787  2020-04-06               South West     34
## 788  2020-04-07               South West     39
## 789  2020-04-08               South West     47
## 790  2020-04-09               South West     24
## 791  2020-04-10               South West     46
## 792  2020-04-11               South West     43
## 793  2020-04-12               South West     23
## 794  2020-04-13               South West     27
## 795  2020-04-14               South West     24
## 796  2020-04-15               South West     32
## 797  2020-04-16               South West     29
## 798  2020-04-17               South West     33
## 799  2020-04-18               South West     25
## 800  2020-04-19               South West     31
## 801  2020-04-20               South West     26
## 802  2020-04-21               South West     26
## 803  2020-04-22               South West     23
## 804  2020-04-23               South West     17
## 805  2020-04-24               South West     19
## 806  2020-04-25               South West     15
## 807  2020-04-26               South West     27
## 808  2020-04-27               South West     13
## 809  2020-04-28               South West     17
## 810  2020-04-29               South West     15
## 811  2020-04-30               South West     26
## 812  2020-05-01               South West      6
## 813  2020-05-02               South West      7
## 814  2020-05-03               South West     10
## 815  2020-05-04               South West     17
## 816  2020-05-05               South West     14
## 817  2020-05-06               South West     19
## 818  2020-05-07               South West     16
## 819  2020-05-08               South West      6
## 820  2020-05-09               South West     11
## 821  2020-05-10               South West      5
## 822  2020-05-11               South West      8
## 823  2020-05-12               South West      7
## 824  2020-05-13               South West      7
## 825  2020-05-14               South West      6
## 826  2020-05-15               South West      4
## 827  2020-05-16               South West      4
## 828  2020-05-17               South West      6
## 829  2020-05-18               South West      4
## 830  2020-05-19               South West      6
## 831  2020-05-20               South West      1
## 832  2020-05-21               South West      9
## 833  2020-05-22               South West      6
## 834  2020-05-23               South West      6
## 835  2020-05-24               South West      3
## 836  2020-05-25               South West      8
## 837  2020-05-26               South West     11
## 838  2020-05-27               South West      5
## 839  2020-05-28               South West     10
## 840  2020-05-29               South West      7
## 841  2020-05-30               South West      3
## 842  2020-05-31               South West      2
## 843  2020-06-01               South West      7
## 844  2020-06-02               South West      2
## 845  2020-06-03               South West      7
## 846  2020-06-04               South West      2
## 847  2020-06-05               South West      2
## 848  2020-06-06               South West      1
## 849  2020-06-07               South West      3
## 850  2020-06-08               South West      3
## 851  2020-06-09               South West      0
## 852  2020-06-10               South West      1
## 853  2020-06-11               South West      2
## 854  2020-06-12               South West      2
## 855  2020-06-13               South West      2
## 856  2020-06-14               South West      0
## 857  2020-06-15               South West      1
## 858  2020-06-16               South West      2
## 859  2020-06-17               South West      0
## 860  2020-06-18               South West      0
## 861  2020-06-19               South West      0
## 862  2020-06-20               South West      2
## 863  2020-06-21               South West      0
## 864  2020-06-22               South West      1
## 865  2020-06-23               South West      1
## 866  2020-06-24               South West      1
## 867  2020-06-25               South West      0
## 868  2020-06-26               South West      3
## 869  2020-06-27               South West      0
## 870  2020-06-28               South West      0
## 871  2020-06-29               South West      1
## 872  2020-06-30               South West      0
## 873  2020-07-01               South West      0
## 874  2020-07-02               South West      0
## 875  2020-07-03               South West      0

1.5 Completion date

We extract the completion date from the NHS Pathways file timestamp:


database_date <- attr(x, "timestamp")
database_date
## [1] "2020-07-02"

The completion date of the NHS Pathways data is Thursday 02 Jul 2020.

1.6 Auxiliary functions

These are functions which will be used further in the analyses.

Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:


## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here

Rsq <- function(x) {
  1 - (x$deviance / x$null.deviance)
}

Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:


## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals

get_r <- function(model) {
  ##  extract coefficients and conf int
  out <- data.frame(r = coef(model))  %>%
    rownames_to_column("var") %>% 
    cbind(confint(model)) %>%
    filter(!grepl("day_of_week", var)) %>% 
    filter(grepl("day", var)) %>%
    rename(lower_95 = "2.5 %",
           upper_95 = "97.5 %") %>%
    mutate(var = sub("day:", "", var))
  
  ## reconstruct values: intercept + region-coefficient
  for (i in 2:nrow(out)) {
    out[i, -1] <- out[1, -1] + out[i, -1]
  }
  
  ## find the name of the intercept, restore regions names
  out <- out %>%
    mutate(nhs_region = model$xlevels$nhs_region) %>%
    select(nhs_region, everything(), -var)
  
  ## find halving times
  halving <- log(0.5) / out[,-1] %>%
    rename(halving_t = r,
           halving_t_lower_95 = lower_95,
           halving_t_upper_95 = upper_95)
  
  ## set halving times with exclusion intervals to NA
  no_halving <- out$lower_95 < 0 & out$upper_95 > 0
  halving[no_halving, ] <- NA_real_
  
  ## return all data
  cbind(out, halving)
  
}

Functions used in the correlation analysis between NHS Pathways reports and deaths:

## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.

getcor <- function(x, ndx) {
  return(cor(x$deaths[ndx],
             x$note_lag[ndx],
             use = "complete.obs",
             method = "pearson"))
}

## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)

getboot <- function(x) {
  result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000), 
                           type = "bca")
  return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
                    r = result$t0,
                    r_low = result$bca[4],
                    r_hi = result$bca[5]))
}

Function to classify the day of the week into weekend, Monday, and the rest:


## Fn to add day of week
day_of_week <- function(df) {
  df %>% 
    dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>% 
    dplyr::mutate(day_of_week = dplyr::case_when(
      day_of_week %in% c("Sat", "Sun") ~ "weekend",
      day_of_week %in% c("Mon") ~ "monday",
      !(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
    ) %>% 
      factor(levels = c("rest_of_week", "monday", "weekend")))
}

Custom color palettes, color scales, and vectors of colors:


pal <- c("#006212",
         "#ae3cab",
         "#00db90",
         "#960c00",
         "#55aaff",
         "#ff7e78",
         "#00388d")

age.pal <- viridis::viridis(3,begin = 0.1, end = 0.7)

3 Comparison with deaths time series

3.1 Outline

We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.

Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.

3.2 Lagged correlation

We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.

First we join the NHS Pathways and death data, and aggregate over all England:

## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max

dth_trunc <- dth %>%
  rename(date = date_report) %>%
  filter(date <= trunc_date) 

## join with notification data
all_data <- x %>% 
  filter(!is.na(nhs_region)) %>%
  group_by(date, nhs_region) %>%
  summarise(count = sum(count, na.rm = T)) %>%
  ungroup %>%
  inner_join(dth_trunc,
             by = c("date","nhs_region"))

all_tot <- all_data %>%
  group_by(date) %>%
  summarise(count = sum(count, na.rm = TRUE),
            deaths = sum(deaths, na.rm = TRUE)) 

We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:


## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
  
  ## lag reports
  summary <- all_tot %>% 
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI
    getboot(.) %>%
    mutate(lag = i)

  lag_cor <- bind_rows(lag_cor, summary)
}

cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
  theme_bw() +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_point() +
  geom_line() +
  labs(x = "Lag between NHS pathways and death data (days)",
       y = "Pearson's correlation") +
  large_txt
cor_vs_lag


l_opt <- which.max(lag_cor$r)

This analysis suggests that the best lag is 23 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 23 days.


all_tot <- all_tot %>%
  rename(date_death = date) %>%
  mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
         note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
         date_note = lag(date_death,16))

lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")

summary(lag_mod)
## 
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -11.5082   -3.3110   -0.4504    3.2358    6.8383  
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 4.750e+00  5.946e-02   79.89   <2e-16 ***
## note_lag    1.325e-05  6.124e-07   21.63   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 17.89637)
## 
##     Null deviance: 9005.1  on 63  degrees of freedom
## Residual deviance: 1170.0  on 62  degrees of freedom
##   (23 observations deleted due to missingness)
## AIC: NA
## 
## Number of Fisher Scoring iterations: 4

exp(coefficients(lag_mod))
## (Intercept)    note_lag 
##  115.630194    1.000013
exp(confint(lag_mod))
##                  2.5 %     97.5 %
## (Intercept) 102.747329 129.722851
## note_lag      1.000012   1.000014

Rsq(lag_mod)
## [1] 0.8700715

mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])

all_tot_pred <- 
  all_tot %>%
  filter(!is.na(note_lag)) %>%
  mutate(pred = mod_fit$fit,
         pred.se = mod_fit$se.fit,
         low = exp(pred - 1.96*pred.se),
         hi = exp(pred + 1.96*pred.se))


glm_fit <- all_tot_pred %>% 
    filter(!is.na(note_lag)) %>%
  ggplot(aes(x = note_lag, y = deaths)) +
  geom_point() + 
  geom_line(aes(y = exp(pred))) + 
  geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
  theme_bw() +
  labs(y = "Daily number of\ndeaths reported",
       x = "Daily number of NHS Pathways reports") +
  large_txt

glm_fit

4 Supplementary figures

4.1 Serial interval distribution

This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.

SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale, w = 0.5)

SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
                                        meanlog = log(4.7),
                                        sdlog = log(2.9), w = 0.5)

SI_dist1 <- data.frame(x = SI_distribution$r(1e5)) 
SI_dist1 <- count(SI_dist1, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 30, 5)) +
    theme_bw()

SI_dist2 <- data.frame(x = SI_distribution2$r(1e5)) 
SI_dist2 <- count(SI_dist2, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
    theme_bw()


ggpubr::ggarrange(SI_dist1,
                  SI_dist2,
                  nrow = 1,
                  labels = "AUTO") 

4.2 Sensitivity analysis - 7 or 21 days moving window

We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.

First with the 7 days window:

## set moving time window (1/2/3 weeks)
w <- 7

# create empty df
r_all_sliding_7days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
plot_R <- r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_7days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_7days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_7 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

Then with the 21 days window:

## set moving time window (1/2/3 weeks)
w <- 21

# create empty df
r_all_sliding_21days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
# plot
plot_R <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_21days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_21days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_21 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

And we combine both outputs into a single plot:


ggpubr::ggarrange(r_R_7,
                  r_R_21,
                  nrow = 2,
                  labels = "AUTO",
                  common.legend = TRUE,
                  legend = "bottom") 

4.3 Correlation between NHS Pathways reports and deaths by NHS region


lag_cor_reg <- data.frame()

for (i in 0:30) {

  summary <-
    all_data %>%
    group_by(nhs_region) %>%
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI for each region
    group_modify(~getboot(.x)) %>%
    mutate(lag = i)
  
  lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}

cor_vs_lag_reg <- 
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
  geom_point() +
  geom_line() +
  facet_wrap(~nhs_region) +
  scale_color_manual(values = pal) +
  scale_fill_manual(values = pal, guide = F) +  
  theme_bw() +
  labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
  theme(legend.position = "bottom") +
  guides(color = guide_legend(override.aes = list(fill = NA)))

cor_vs_lag_reg

5 Export data

We save the tables created during our analysis:


if (!dir.exists("excel_tables")) {
  dir.create("excel_tables")
}


## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")

for (e in tables_to_export) {
  rio::export(get(e),
              file.path("excel_tables",
                        paste0(e, ".xlsx")))
}

## also export result from regression on lagged data 
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))

6 System information

6.1 Outline

The following information documents the system on which the document was compiled.

6.2 System

This provides information on the operating system.

Sys.info()
##                                                                                            sysname 
##                                                                                           "Darwin" 
##                                                                                            release 
##                                                                                           "19.5.0" 
##                                                                                            version 
## "Darwin Kernel Version 19.5.0: Tue May 26 20:41:44 PDT 2020; root:xnu-6153.121.2~2/RELEASE_X86_64" 
##                                                                                           nodename 
##                                                                                   "Mac-1750.local" 
##                                                                                            machine 
##                                                                                           "x86_64" 
##                                                                                              login 
##                                                                                             "root" 
##                                                                                               user 
##                                                                                           "runner" 
##                                                                                     effective_user 
##                                                                                           "runner"

6.3 R environment

This provides information on the version of R used:

R.version
##                _                           
## platform       x86_64-apple-darwin17.0     
## arch           x86_64                      
## os             darwin17.0                  
## system         x86_64, darwin17.0          
## status                                     
## major          4                           
## minor          0.2                         
## year           2020                        
## month          06                          
## day            22                          
## svn rev        78730                       
## language       R                           
## version.string R version 4.0.2 (2020-06-22)
## nickname       Taking Off Again

6.4 R packages

This provides information on the packages used:

sessionInfo()
## R version 4.0.2 (2020-06-22)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Catalina 10.15.5
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggnewscale_0.4.1     ggpubr_0.4.0         lubridate_1.7.9     
##  [4] chngpt_2020.5-21     cyphr_1.1.0          DT_0.14             
##  [7] kableExtra_1.1.0     janitor_2.0.1        remotes_2.1.1       
## [10] projections_0.5.1    earlyR_0.0.1         epitrix_0.2.2       
## [13] distcrete_1.0.3      incidence_1.7.1      rio_0.5.16          
## [16] reshape2_1.4.4       rvest_0.3.5          xml2_1.3.2          
## [19] linelist_0.0.40.9000 forcats_0.5.0        stringr_1.4.0       
## [22] dplyr_1.0.0          purrr_0.3.4          readr_1.3.1         
## [25] tidyr_1.1.0          tibble_3.0.1         ggplot2_3.3.2       
## [28] tidyverse_1.3.0      here_0.1             reportfactory_0.0.5 
## 
## loaded via a namespace (and not attached):
##  [1] nlme_3.1-148      fs_1.4.2          webshot_0.5.2     httr_1.4.1       
##  [5] rprojroot_1.3-2   tools_4.0.2       backports_1.1.8   utf8_1.1.4       
##  [9] R6_2.4.1          mgcv_1.8-31       DBI_1.1.0         colorspace_1.4-1 
## [13] withr_2.2.0       gridExtra_2.3     tidyselect_1.1.0  sodium_1.1       
## [17] curl_4.3          compiler_4.0.2    cli_2.0.2         labeling_0.3     
## [21] matchmaker_0.1.1  scales_1.1.1      digest_0.6.25     foreign_0.8-80   
## [25] rmarkdown_2.3     pkgconfig_2.0.3   htmltools_0.5.0   dbplyr_1.4.4     
## [29] htmlwidgets_1.5.1 rlang_0.4.6       readxl_1.3.1      rstudioapi_0.11  
## [33] farver_2.0.3      generics_0.0.2    jsonlite_1.7.0    crosstalk_1.1.0.1
## [37] car_3.0-8         zip_2.0.4         kyotil_2019.11-22 magrittr_1.5     
## [41] Matrix_1.2-18     Rcpp_1.0.4.6      munsell_0.5.0     fansi_0.4.1      
## [45] viridis_0.5.1     abind_1.4-5       lifecycle_0.2.0   stringi_1.4.6    
## [49] yaml_2.2.1        carData_3.0-4     snakecase_0.11.0  MASS_7.3-51.6    
## [53] plyr_1.8.6        grid_4.0.2        blob_1.2.1        crayon_1.3.4     
## [57] lattice_0.20-41   cowplot_1.0.0     splines_4.0.2     haven_2.3.1      
## [61] hms_0.5.3         knitr_1.29        pillar_1.4.4      boot_1.3-25      
## [65] ggsignif_0.6.0    reprex_0.3.0      glue_1.4.1        evaluate_0.14    
## [69] data.table_1.12.8 modelr_0.1.8      vctrs_0.3.1       selectr_0.4-2    
## [73] cellranger_1.1.0  gtable_0.3.0      assertthat_0.2.1  xfun_0.15        
## [77] openxlsx_4.1.5    broom_0.5.6       rstatix_0.6.0     survival_3.1-12  
## [81] viridisLite_0.3.0 ellipsis_0.3.1